Dice game

ABSTRACT

A dice game comprises first and second octahedron dice producing first and second results, respectively, and a croupier-type gaming table having a plurality of bet lines, each of the bet lines corresponding to at least one of the first result and the second result, or a sum of the first and second results. A method of playing a dice game comprises placing a wager on at least one bet line of a croupier-type gaming table, rolling a pair or octahedron dice, wherein the first octahedron die provides a first result, the second octahedron die provides a second result, and the sum of the first result and second result represents a roll total, and determining if the wager wins, loses, or pushes in response to at least one of the first result, second result, and roll total. Because of the rules governing abstracts, this abstract should not be used to construe the claims.

BACKGROUND

The present invention relates generally to a dice game and more particularly to the use of octahedron die with a croupier type gaming table.

Traditional craps (i.e., “Bank Craps”) is arguably the most popular game offered for play by a casino, in part because it offers players better odds of winning as compared to other games. In traditional craps, a pair of six-sided (i.e., hexahedral) dice are rolled on a croupier type gaming table. The surface of the table includes specific markings representing different results of the rolled dice. FIG. 11, for example, illustrates a portion of a table used for traditional craps.

The player rolling the dice is known as the “shooter”. The shooter attempts to establish a “point” number on his first roll (i.e., the “come out roll”) and then match his point number (i.e., “make his point”) on subsequent rolls prior to rolling a seven (i.e., “sevens out”). Only the numbers ‘4’, ‘5’, ‘6’, ‘8’, ‘9’, or ‘10’ can be a point number. If the shooter rolls one of these numbers on the come out roll, he establishes the point. If the shooter makes his point, he retains the dice and a new game begins (i.e., his next immediate roll is a new come out roll that establishes a new point). If the shooter “sevens out” (i.e., fails to make his point), the dice are passed to a new shooter and a new game begins.

Prior to a come out roll, a shooter must (and other players may) place a “line bet” (i.e., place a wager on the “pass line” and/or on the “don't pass line”). If the shooter rolls a ‘7’ or ‘11’ on the come out roll, wagers placed on the pass line win and wagers placed on the don't pass line lose. Rolling the numbers ‘2’, ‘3’, or ‘12’ on the come out roll is know as “rolling craps”. If the shooter rolls a ‘2’ or ‘3’ on the come out roll, wagers placed on the pass line lose and wagers placed on the don't pass line win. As illustrated in FIG. 11, the “don't pass line” includes a “bar 12.” Thus, if the shooter rolls a ‘12’ on the come out roll, wagers placed on the pass line lose and wagers placed on the don't pass line push (i.e., the wager neither wins or loses on the come out roll but is decided by subsequent rolls). It should be apparent to one skilled in the art that the description above is general in nature and that other rules and possible bets and/or wages have been omitted.

FIG. 10 illustrates the possible combinations of roll results for traditional craps which uses a pair of six-sided dice. As seen in FIG. 10, there are thirty-six possible combinations that may be rolled using the pair of six-sided dice. The roll total of each die combination is between two (e.g., both die rolled are ‘1’) and twelve (i.e., both die rolled are ‘6’). Table 1 below lists the total, the number of ways that the roll total may be obtained, and the odds of obtaining the particular roll total. For example (referring to FIG. 10), there are three different combinations of roll results (i.e., 1-3, 2-2, and 3-1) that produce a roll total of four (‘4’). Thus, the odds of rolling a four (‘4’) are 0.083333 (i.e., 3/36). As a further example, there are six different combinations of roll results (i.e., 1-6, 2-5, 3-4, 4-3, 5-2, and 6-1) that produce a roll total of seven (‘7’). Thus, the odds of rolling a seven (‘7’) are 0.166666 (i.e., 6/36). TABLE 1 Odds of Rolling a Particular Number With a Pair of Hexahedral Dice Roll Total Number of Ways Odds 2 1 0.027777 3 2 0.055555 4 3 0.083333 5 4 0.111111 6 5 0.138888 7 6 0.166666 8 5 0.138888 9 4 0.111111 10 3 0.083333 11 2 0.055555 12 1 0.027777

In traditional craps, a roll total of seven (‘7’) is the plurality or “miss out” number (6 out of 36 or 16.6%). The spread between the odds of hitting the miss out number (i.e., rolling a ‘7’) and either of its nearest roll total outcomes (i.e., rolling a ‘6’ or ‘8’) is 2.7778% (i.e., 16.6666%-13.8888%). This spread allows a casino to establish acceptable payoff odds (i.e., payoff odds are typically chosen such that the house has neither too much advantage so as to discourage play, nor too much of a disadvantage so as to lose money). For example, the casino may pay four dollars for every dollar bet (i.e., a 4-to-1 payoff) should a player match any roll that totals seven (7).

Even though the chances of winning while playing traditional craps are greater than many other casino games, many players seek games that offer an even better chance of winning. Accordingly, a need exists for a game that offers better odds to the player than does traditional craps, yet maintains a sufficient advantage to the casino, and overcomes the limitations inherent in prior art.

SUMMARY

One aspect of the invention relates to a dice game comprising a first octahedron die for producing a first result, a second octahedron die for producing a second result, and a croupier-type gaming table having a plurality of bet lines, wherein each of the bet lines corresponds to at least one of the first result and the second result, or a sum of the first result and the second result.

Another aspect of the invention relates to a method of playing a dice game comprising placing a wager on at least one bet line of a croupier-type gaming table, rolling a pair or octahedron dice, wherein the first octahedron die provides a first result, the second octahedron die provides a second result, and the sum of the first result and the second result represents a roll total, and determining if the wager wins, loses, or pushes in response to at least one of the first result, the second result, and the roll total.

Another aspect of the invention relates to a method for modeling a roll of a pair of octahedron dice comprising establishing a plurality of ranges, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one of a plurality of possible roll totals, randomly sampling a uniformly distributed number, selecting the range containing the randomly sampled, uniformly distributed number, and providing the roll total associated with the selected range.

Another aspect of the invention relates to a method for modeling a roll of a plurality of octahedron dice comprising determining a roll result for one octahedron die, wherein the determining comprises, establishing eight equally sized ranges between zero and one, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one possible roll result for the one octahedron die, randomly sampling a uniformly distributed number between zero and one, selecting the range containing the sampled uniformly distributed number, and providing the roll result associated with the selected range, and repeating the determining for each of the remaining plurality of octahedron dice.

Another aspect of the invention relates to a module containing an ordered set of instructions that when executed perform a method of playing a dice game, said method comprising receiving wager information, electronically providing at least one of a first result for a roll of a first octahedron die, a second result for a roll of a second octahedron die, and a roll total, said roll total equaling the sum of said first result and said second result, and determining if the wager wins, loses, or pushes in response to at least one of the first result, the second result, and the roll total.

Another aspect of the invention relates to a method of playing a dice game in an electronic format comprising inputting wager information, receiving the results of an electronic simulation of a roll of a pair of octahedron dice, wherein said results include at least one of a first result for the roll of the first octahedron die, a second result for the roll of the second octahedron die, and a roll total, said roll total equaling the sum of said first result and said second result, and receiving a determination as to whether said wager wins, loses, or pushes in response to at least one of the first result, the second result, and the roll total.

BRIEF DESCRIPTION OF THE DRAWINGS

To enable the present invention to be easily understood and readily practiced, the present invention will now be described for purposes of illustration and not limitation, in connection with the following figures wherein:

FIG. 1 is a perspective view of a octahedron die according to one embodiment.

FIG. 2 is a top-view of the octahedron die of FIG. 1 according to one embodiment.

FIG. 3 is a bottom-view of the octahedron die of FIG. 1 according to one embodiment.

FIG. 4 illustrates the possible combinations of roll results for a pair of octahedron dice.

FIG. 5 is a simplified diagram of a portion of a gaming table according to one embodiment.

FIG. 6 illustrates a method for adapting a dice game into an electronic format.

FIG. 7 is a simplified, perspective view of a video machine for playing a dice game according to one embodiment.

FIG. 8 is a simplified, perspective view of a personal computer for playing a dice game according to one embodiment.

FIG. 9 is a simplified view of a web-based system for playing a dice game according to one embodiment.

FIG. 10 illustrates the possible combinations of roll results for a pair of hexahedral dice.

FIG. 11 is a simplified diagram of a portion of a prior art gaming table.

DETAILED DESCRIPTION

The detailed description sets forth specific embodiments which are described in sufficient detail to enable those skilled in the art to practice the present invention. It should be apparent to those skilled in the art that other embodiments may be utilized, and that certain changes may be made, while remaining within the scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the invention is defined only by the appended claims.

FIGS. 1-3 are perspective, top, and bottom views, respectively, of an octahedron die 1 according to one embodiment. The octahedron die 1 has eight faces. In the current embodiment, the faces are numbered ‘1’ through ‘8’ with (as best seen in FIGS. 2 and 3) the odd numbers ‘1’, ‘3’, ‘5’, and ‘7’ located on the “top” half of the die 1 and the even numbers ‘2’, ‘4’, ‘6’, and ‘8’ located on the “bottom” half of the die 1. It should be apparent to one skilled in the art that the particular indicia scheme used for the faces may be varied while remaining within the scope of the present invention.

The octahedron die 1 is a regular, convex polyhedra. A polyhedron refers to a three-dimensional solid which consists of a collection of polygons, usually joined at their edges. The octahedron die 1 (being a regular, convex polyhedra) is geometrically perfect. The die 1 possesses symmetry, a unique center of gravity, and lies flat and flush when at rest. All edges are the same length and each face is an equilateral triangle. The octahedron die 1 includes eight (8) faces, twelve (12) edges, and six (6) vertices (where a vertex refers to a point at which three of more edges of a polyhedron meet). The octahedron die 1 is an isohedrea which comports with Euler's Equation (i.e., Vertices+Faces−Edges=2); thus, the octahedron die 1 has “duality”. Because the octahedron die 1 comports with Euler's Equation, the probability of any one number being rolled is the same as each of the other numbers (i.e., the octahedron die 1 is said to be implicitly “fair”). For example, when the die 1 is rolled, it is just as likely that the result will be a ‘2’ as it is that the result will be a ‘3’.

FIG. 4 illustrates the possible combinations of roll results for a pair of octahedron dice 1. As seen in FIG. 4, there are sixty-four possible combinations that may be rolled using a pair of octahedron dice 1. The roll total of each combination is between two (e.g., the result for each die rolled is ‘1’) and sixteen (i.e., the result for each die rolled is ‘8’). Table 1 below lists the roll total, the number of ways that the roll total may be obtained, and the odds of obtaining the particular roll total. For example (referring to FIG. 4), there are three different combinations of roll results (i.e., 1-3, 2-2, and 3-1) that produce a roll total of four (‘4’). Thus, the odds of rolling a four (‘4’) are 0.046875 (i.e., 3/64). As a further example, there are eight different combinations of roll results (i.e., 1-8, 2-7, 3-6, 4-5, 5-4, 6-3, 7-2, and 8-1) that produce a roll total of nine (‘9’). Thus, the odds of rolling a nine (‘9’) are 0.125000 (i.e., 8/64). TABLE 2 Odds of Rolling a Particular Number With a Pair of Octahedron Dice Roll Total Number of Ways Odds 2 1 0.015625 3 2 0.031250 4 3 0.046875 5 4 0.062500 6 5 0.078125 7 6 0.093750 8 7 0.109375 9 8 0.125000 10 7 0.109375 11 6 0.093750 12 5 0.078125 13 4 0.062500 14 3 0.046875 15 2 0.031250 16 1 0.015625

In the current embodiment, a roll total of nine (‘9’) is the plurality or “miss out” number (8 out of 64 or 12.5%). The spread between the odds of hitting the miss out number (i.e., ‘9’) and either of its nearest roll total outcomes (i.e., ‘8’ or ‘10’) is 1.5625% (i.e., 12.5%-10.9375%). This spread allows the casino enough “room” to establish acceptable payoff odds (i.e., payoff odds which give the house enough advantage to make money, but not too much advantage so as to discourage play).

FIG. 5 is a simplified diagram of a gaming table 10 according to one embodiment. The gaming table 10 includes a pass line 12, don't pass line 14, a field line 16, come line 18, don't come line 20, point boxes 22, and proposition bet lines 24. The gaming table 10 may be used in conjunction with a pair of octahedron dice 1 (as discussed above in conjunction with FIGS. 1-4) to provide a dice game according to one embodiment. It should be apparent to one skilled in the art that the markings on the table may be adapted as necessary to correspond with the specific indicia chosen for use on the octahedron dice 1.

In the current embodiment, the field line includes numbers 2, 3, 4, 5, 6, 11, 12, 13, 14, 15, and 16. A player placing a “field bet” wins if the roll total of the shooter's immediate next roll matches any one of the field numbers. If the shooter rolls a nine (i.e., nines-out) or any other number not within the field line (e.g., ‘7’, ‘8’, ‘10’), the field bet is lost. Typically, the field bet payoff is 1-to-1, however, for a roll of 2 or 16 the payoff is typically 2-to-1.

The point boxes 22 included boxes for numbers 4, 5, 6, 7, 8, 10, 11, 12, 13, and 14. If a shooter rolls a ‘4’, ‘5’, ‘6’, ‘7’, ‘8’, ‘10’, ‘11’, ‘12’, ‘13’, and ‘14’ on the come out roll, a point is established. A disk or puck (not shown) may be located by the game operator (for example, the “dealer”) on the appropriate point box to track the shooter's current point number. For example, if the shooter rolls an ‘8’ on the come out roll, the puck is placed on the point box having the number 8 therein.

After a point is established, a player may make a “place bet” on one or more of the point boxes prior to a subsequent roll. For example, after the shooter establishes ‘8’ as his point number as discussed above, the dealer sets the puck on the point box with the number 8 therein. A player may then make a place bet, for example, on the number 7. If the shooter rolls a ‘7’ on the next immediate roll, the player's place bet wins. If, however, the shooter makes his point (e.g., rolls an ‘8’) on the next roll or rolls any of the other numbers in the point boxes (i.e., rolls a ‘4’, ‘5’, ‘6’, ‘7’, ‘10’, ‘11’, ‘12’, ‘13’, or ‘14’), the player's place bet pushes (i.e., the player does not lose his place bet, but does not receive any additional payout). After a win or push, the player can either remove his place bet or “let it ride.” If the shooter rolls a ‘9’ (i.e., nines-out) while a place bet wager is active, the player loses the place bet.

After the shooter establishes his point, a player may make a “come bet” by placing a wager on the come line. If the shooter craps-out (i.e., rolls a ‘2’, ‘3’, or ‘16’) on the next roll, the player loses his come bet; if the shooter rolls a ‘9’ (i.e., nines-out) on the next roll, the player will win (typically the payoff is 1-to-1); and if the shooter makes his point or rolls one of the other numbers in the point boxes (i.e., rolls a ‘4’, ‘5’, ‘6’, ‘7’, ‘8’, ‘10’, ‘11’, ‘12’, ‘13’, or ‘14’), a “come point” is established and the player's come bet is moved from the come line to the point box corresponding to the number that the shooter rolled. Once the players come bet is moved to the point box it remains there unless the shooter rolls that number again (i.e., “makes the come point”) or rolls a “9” (i.e., nines-out).

For example, assume that the shooter has established seven as the point (i.e., rolled a ‘7’ on the come out roll). Prior to the next roll, assume further that a player makes a come bet by putting a wager on the come line. If the shooter craps-out on the next roll (i.e., rolls a ‘2’, ‘3’, or ‘16’), the player loses the come bet. If the shooter rolls a ‘9’ (i.e., nines-out) on the next roll, however, the player receives a 1-to-1 payoff. If the shooter rolls a ‘4’, ‘5’, ‘6’, ‘7’, ‘8’, ‘10’, ‘11’, ‘12’, ‘13’, or ‘14’ (i.e., establishes a “come point”), the player's come bet is moved from the come line to the appropriate point box. For example if the shooter rolls an ‘11’, the player's “come point” is established as ‘11’ and his wager is moved from the come line to the point box with the number 11 therein. The wager remains on point box 11 until the shooter either nines-out, in which case the wager is lost, or rolls the number “11” (i.e., “making the come point”), in which case the wager wins and the player receives a payoff.

Additionally, after the shooter establishes his point, a player may make a “don't come bet” by placing a wager on the don't come line. In the current embodiment, the “don't come” line includes “Bar 16.” Thus, if the shooter craps-out by rolling a ‘16’, any wagers placed on the don't come line push (i.e., neither win nor lose). If the shooter craps-out by rolling a ‘2’ or ‘3’ on the next roll, the player wins his don't come bet; if the shooter rolls a ‘9’ on the next roll, the player loses his don't come bet; and, if the shooter makes his point or rolls one of the other numbers in the point boxes (e.g., ‘4’, ‘5’, ‘6’, ‘7’, ‘8’, ‘10’, ‘11’, ‘12’, ‘13’, or ‘14’), a “don't come point” is established and the player's don't come bet is moved from the don't come line to the point box corresponding to the number that the shooter rolled. Once the player's don't come bet is moved to the point box, the player wins if the shooter rolls a ‘9’ (i.e., nines-out) prior to rolling the don't come point. If the shooter matches the don't come point prior to rolling a ‘9’, however, the player loses his don't come bet.

In the current embodiment, the proposition bet lines 24 include “Hardway” boxes, an “Any 4” box, “Horn Bet” boxes, an “Any 2, 3, 16” box, and a “Big 8-10” circle. A player placing a wager on the hardway “5-5 box”, for example, wins if the shooter rolls double fives (i.e., 5-5). If the shooter rolls a ‘10’ in some other combination (e.g., 2-8, 3-7, 4-6, 6-4, 7-3, 8-2) or rolls a ‘9’ (i.e., nines-out), however, the wager placed on the hardway “5-5 box” is lost. If the shooter rolls any other combination (i.e., a roll other than a ‘9’ or a ‘10’), the player can either remove his wager from the hardway “5-5 box” before the next roll or he may “let it ride.” The other hardway proposition bets may be played in a similar manner.

A player placing a wager on the “Any 4” box wins if the shooter rolls a ‘4’ in any combination (i.e., 1-3, 2-2, or 3-1) on the next immediate roll. If the shooter rolls any other combination, the wager on the “Any 4” is lost. A player placing a wager on one of the “Horn Bet” boxes, for example the “horn box 3”, wins if the shooter rolls a ‘3’ in any combination (i.e., 1-2 or 2-1) on the next immediate roll. If the shooter rolls any other combination, the wager placed on the “horn box 3” is lost. A player placing a wager on the “Any 2, 3, 16” box wins if the shooter rolls a ‘2’, ‘3’, or ‘16’ in any combination (i.e., 1-1, 1-2, 2-1, or 8-8) on the next immediate roll. If the shooter rolls any other combination, the wager on the “Any 2, 3, 16” is lost. A player placing a wager on the “Big 8” or “Big 10” circle will win if the shooter rolls an ‘8’ or a ‘10’, respectively, in any combination (i.e., 1-7, 2-6, 3-5, 4-4, 5-3, 6-2, 7-1, 2-8, 3-7, 4-6, 5-5, 6-4, 7-3, 8-2) on the next immediate roll. It the shooter rolls any other combination, the wager on the “Big 8” or “Big 10” circle is lost.

It should be apparent to those of ordinary skill in the art that other types of bets or wagers may be made while remaining within the scope of the present invention and that the specific wagers discussed above have been provided for exemplary purposes and are not intended to be limiting in any manner.

Furthermore, it should be apparent to one skilled in the art that a dice game employing one or more octahedron die 1 (e.g., as discussed above in conjunction with FIGS. 1-5) may be adapted for play in an electronic format. For example, a dice game employing one or more octahedron die 1 may be adapted for play on a hand-held gaming device (e.g., Nintendo GameBoy®, a cell phone, etc.), a television-based gaming system (e.g., Sony Playstation®, Microsoft X-Box®, Nintendo Gamecube®, etc.), a stand-alone video machine, a personal computer, and/or via an on-line network connection (e.g., the internet), among others.

FIG. 6 illustrates a method 30 for determining a roll total for a dice game using a pair of octahedron dice 1 according to one embodiment. For use in an electronic format, method 30 may be executed using one or more software modules, one or more hardware modules, or a combination of one or more software and/or hardware modules, among others. In the current embodiment, a module refers to an ordered set of instructions (among others), which when executed, performs a specific task.

Method 30 may begin with operation 31 wherein a roll is initiated. For example, a roll may be initiated by a command which is automatically executed by computer programming code. As another example, a player may initiate the roll by providing an input such as pressing a designated button on a video game, keyboard, etc. which signifies that the dice should be rolled.

Operational control then passes to operation 32 in which a uniformly distributed number (designated herein as “e”) between 0 and 1 is randomly sampled. A uniform distribution refers to the situation in which each result is equally as likely to be sampled as any other possible result. In one embodiment, a uniform random number generator (e.g., RAND in Microsoft's EXCEL® Toolkit Package) may be used to randomly sample the number “e”. It should be noted that other methods of randomly selecting a uniformly distributed number “e” may also be used while remaining within the scope of the present invention.

Operational control then passes to operation 33 in which a roll total is assigned in response to the sampling of the uniformly distributed number, “e”. The specific roll total assigned depends upon the probability of rolling a specific roll total. More specifically, a plurality of ranges, each containing at least one uniformly distributed number between 0 and 1, is established and associated with one of a plurality of possible roll totals.

For example in the current embodiment, fifteen ranges are established (i.e., one or each possible roll total of the pair of octahedron dice 1) are established. The size of each range depends upon the probability of rolling the particular roll total associated with the range. Table 3 lists the roll totals assigned for a particular range of randomly sampled numbers according to one embodiment.

The probability of rolling a ‘9’ using a pair of octahedron dice 1 is 0.125000 (as discussed above in conjunction with Table 2). Accordingly, the uniformly distributed numbers that are greater than or equal to zero but less than or equal to 0.125000 are grouped in a range that corresponds to the roll total ‘9’. Thus, if the randomly sampled number “e” is greater than zero and less than or equal to 0.125000, the roll total ‘9’ is assigned by operation 33.

Additionally, the uniformly distributed numbers that are greater than 0.125000 but less than and equal to 0.234375 are grouped in a range that correspond to the roll total ‘8’. The number 0.234375 is derived by adding the probability of rolling an ‘8’ (i.e., 0.109375, as seen in Table 2) to the probability of rolling a ‘9’ (i.e., 0.125000 as seen in Table 2). Thus, if the randomly sampled number “e” is greater than 0.125000 but less than and equal to 0.234375, the roll total ‘8’ is assigned by operation 33.

Additionally, the uniformly distributed numbers that are greater than 0.234375 but less than or equal to 0.343750 are grouped in a range that corresponds to the roll total ‘10’. The number 0.343750 is derived by adding the probability of rolling a ‘10’ (i.e., 0.109375, as seen in Table 2) to the cumulative sum of probabilities for the roll totals previously ranged (i.e., 0.234375; the sum of the probabilities of rolling a ‘9’ and an ‘8’). Thus, if the randomly sampled number “e” is greater than 0.234375 but less than or equal to 0.343750, the roll total ‘10’ is assigned by operation 33.

Additionally, the uniformly distributed numbers that are greater than 0.343750 and less than or equal to 0.437500 are grouped in a range that corresponds to the roll total ‘7’. The number 0.437500 is derived by adding the probability of rolling a ‘7’ (i.e., 0.093750, as seen in Table 2) to the cumulative sum of probabilities for the roll totals previously ranged (i.e., 0343750, the sum of the probabilities of rolling a ‘9’, an ‘8’, and a ‘10’). Thus, if the randomly sampled number “e” is greater than 0.343750 and less than or equal to 0.437500, the roll total ‘7’ is assigned by operation 33.

It should be apparent to one skilled in the art that this pattern is repeated for each of the roll totals as illustrated in Table 3. Furthermore, it should be apparent to one skilled in art that the particular order in which the ranges are established may be altered while remaining within the scope of the present invention and that the particular order illustrated in Table 3 is for exemplary purposes and not meant to limit the present invention. TABLE 3 Assigned Roll Totals Relative to Randomly Sampled Number “e” Roll Total Randomly Sampled Assigned Number (e) 2 0.968750 < e ≦ 0.984375 3 0.906250 < e ≦ 0.937500 4 0.812500 < e ≦ 0.859375 5 0.687500 < e ≦ 0.750000 6 0.531250 < e ≦ 0.609375 7 0.343750 < e ≦ 0.437500 8 0.125000 < e ≦ 0.234375 9 0.000000 ≦ e ≦ 0.125000 10 0.234375 < e ≦ 0.343750 11 0.437500 < e ≦ 0.531250 12 0.609375 < e ≦ 0.687500 13 0.750000 < e ≦ 0.812500 14 0.859375 < e ≦ 0.906250 15 0.937500 < e ≦ 0.968750 16 0.984375 < e ≦ 1.000000

The current embodiment may be integrated into a computer program which, for example, can complete thousands of rolls in a short period of time on a computer system. The computer program may, for example, be used to verify the various odds occasioned by a dice game employing a pair of octahedron dice 1. It should be apparent to one skilled in the art that other uses for the current embodiment are also within the scope of the present invention.

In an alternative embodiment, a roll between ‘1’ and ‘8’ (e.g., representing the roll of a single die from a pair of octahedron dice 1) is assigned. In this alternative embodiment, the probability of obtaining one roll result is the same as obtaining any other roll result (e.g., the probability of rolling a ‘1’ is 0.125, a ‘2’ is 0.125, a ‘3’ is 0.125, etc.). Thus, each range of randomly sampled numbers “e” will be the same size. For example, if the randomly sampled number “e” is greater than zero and less than or equal to 0.125, the roll is set to ‘1’. If the randomly sampled number “e” is greater than 0.125 and less than or equal to 0.250, the roll is set to ‘2’. If the randomly sampled number “e” is greater than 0.250 and less than or equal to 0.375, the roll is set to ‘3’. This pattern continues until the roll is set to ‘8’ for the randomly sampled number “e” that is greater than 0.875 and less than or equal to 1.

As mentioned above, the roll assigned in this alternative embodiment represents the roll for a single die of a pair of octahedron dice 1. Accordingly, this process may be repeated to obtain the roll results for additional octahedron dice 1. In the current embodiment, the process is repeated to obtain the roll result for a second octahedron die 1. The roll results for the first and second die may then be added together to obtain a final roll total. It should be apparent to one skilled in the art that this alternative embodiment can be repeated as many times as desired, for example, to simulate the rolling of any number of octahedron dice 1.

After the roll total is assigned in operation 33, operational control is passed to operation 34 which displays the result. For example, the roll total for the pair of octahedron dice 1 may be displayed on a computer monitor or on a video game display, among others. As another example, the roll total for each individual octahedron die 1 (e.g., as found using the alternative embodiment discussed above) may be displayed on a computer monitor or on a video game display, among others.

In addition to, or instead of, being displayed, the roll result may be used as input for other software or hardware modules. One or more of such software modules may, for example, contain a series of instructions corresponding to the dice game discussed above in conjunction with FIGS. 1-5. These one or more software modules may be operable to determine whether the particular roll total signifies that a player's wager is a winner (and possibly also determine the payoff amount) or a loser. It should be apparent to one skilled in the art the method 30 may be implemented using one or more software modules, one or more hardware modules, or one or more software and hardware modules in combination.

FIG. 7 is a simplified, perspective view of a video machine 40 for playing a dice game according to one embodiment. Video machine 40 includes a cabinet 41 which houses a monitor 42, control buttons 43, and lockable box 44. The cabinet 41 also houses a central processing unit (CPU) (not shown), data storage unit (e.g., a hard drive, ZIP drive, floppy drive, CD/DVD drive, tape drive, memory, etc.) (not shown), graphics card (not shown), and communication device (e.g., modem, network interface card, etc.) (not shown), among others. In the current embodiment, the data storage unit, communication device, graphics card, etc. are responsive to the CPU. A computer program, for example, having a module encoding the rules for the dice game and for determining a roll total, may reside on the data storage unit. The CPU is operable, for example, to receive input (for example, from control buttons 43), execute the computer program residing on the data storage unit, and output results to the monitor 42 via the graphics card.

A graphical depiction of the gaming table 10 (e.g., as discussed above in conjunction with FIG. 5), a graphical depiction of the result of a roll of a pair of octahedron dice 1 (e.g., as discussed above in conjunction with FIG. 1), and a graphical depiction of a players wagers, among others, may be displayed by monitor 42. Control buttons 43 may be used by a player to designate certain actions during the game. For example, control buttons 43 may be used to begin or end a game, place and revoke wagers, and initiate a dice roll, among others.

In the current embodiment, lockable box 44 includes a slot 46 for accepting and dispensing cash or tokens and/or a card reader 45 for debiting and crediting points/money to a game card/credit card. The video machine 40 may operate independently or be networked to another machine via the communication device. For example, the networked video machine 40 may be connected to a server so that a casino operator can track the gaming habits of a particular player. A player opening an account with the casino is issued a game card which may identify the player and maintain records of the player's account balance, the type of games played, and the type of bets made at each game, among others. When the player inserts his game card into card reader 45, these records may be retrieved, monitored, updated, etc. by the casino operator.

FIG. 8 is a simplified, perspective view of a computer system 50 for playing a dice game according to one embodiment. In the current embodiment, the computer system 50 includes housing 52, monitor 54, keyboard 56, and mouse 58. In the current embodiment, the housing 52 contains a processor (CPU) (not shown), a memory (not shown), a data storage device (for example, a hard drive, ZIP drive, floppy drive, CD/DVD drive, tape drive, memory, etc.) (not shown), graphics card (not shown) and a communication device (e.g., modem, network interface card, etc.) (not shown), among others.

In the current embodiment, the data storage unit, communication device, graphics card, etc. are responsive to the CPU. A computer program, for example, having a module encoding the rules for the dice game and for determining a roll total, may reside on the data storage unit or be read from a CD/DVD drive. The CPU is operable to receive input (for example, from keyboard 56), execute the computer program residing on the data storage unit, and output results to the monitor 54 via the graphics card.

A graphical depiction of the gaming table 10 (e.g., as discussed above in conjunction with FIG. 5), a graphical depiction of the result of a roll of a pair of octahedron dice 1 (e.g., as discussed above in conjunction with FIG. 1), and a graphical depiction of a players wagers, among others, may be displayed by monitor 54. The keyboard 56 may be used by a player to designate certain actions during the game. For example, specific keystrokes may be used to begin or end a game, place and revoke wagers, and initiate a dice roll, among others.

FIG. 9 is a simplified view of a Internet-based system 60 for playing a dice game according to one embodiment. The Internet-base system 60 is used for illustrative purposes only to facilitate an understanding of the invention. It should be apparent to one skilled in the art, however, that other computer network types may be used while remaining within the scope of the present invention.

FIG. 9 illustrates a client-server model for communicating via the Internet. Computer 66 and server 62 are operable to exchange information via the internet 64, for example, using world-wide-web (WWW) protocols (e.g., hyper text transfer protocol (HTTP); file transfer protocol (FTP), etc.).

Client computer 66 may be any laptop, desktop, work-station, or other device capable of accessing the Internet 64. Client computer 66 may include a processor (CPU) (not shown), a memory (not shown), a data storage device (for example, a hard drive, ZIP drive, floppy drive, CD/DVD drive, tape drive, memory, etc.) (not shown), graphics card (not shown), display, keyboard, mouse, and a communication device (e.g., modem, network interface card, etc.) (not shown), among others. The client computer's 66 storage device may contain one or more programs or modules, executed by the client computer's 66 CPU, operable to facilitate communication with the server 62.

Server 62 may include a processor (CPU) (not shown), a memory (not shown), a data storage device (for example, a hard drive, ZIP drive, floppy drive, CD/DVD drive, tape drive, memory, etc.) (not shown), graphics card (not shown), display (not shown), keyboard (not shown), mouse (not shown), and a communication device (e.g., modem, network interface card, etc.) (not shown), among others. The server's data storage device may contain one or more programs or modules operable to implement the functions of the dice game according to one embodiment. The programs may have, for example, a module encoding the rules for the dice game and for determining a roll total. The programs and modules are executed by server's CPU.

In the current embodiment, the client computer 66 executes a program and/or module and transmits information though the Internet 64 requesting service from a program that is executed on the server 62. In response to the information transmitted by the client computer 66, the server 62 returns information (e.g., data files, results from the programs executed by the server 62, etc.) to the client computer 66. The client computer 66 may display and/or further process the information received from the server 62.

It should be recognized that the above-described embodiments of the invention are intended to be illustrative only. Numerous alternative embodiments may be devised by those skilled in the art without departing from the scope of the following claims. 

1. A dice game, comprising: a first octahedron die for producing a first result; a second octahedron die for producing a second result; and a croupier-type gaming table having a plurality of bet lines, wherein each of said bet lines corresponds to at least one of said first result and said second result, or a sum of said first result and said second result.
 2. The dice game of claim 1 wherein said first die and said second die each have eight faces, each face having identifying indicia thereon.
 3. The dice game of claim 1 wherein said first die and said second die are identical, each die having eight faces, each face having thereon a unique numeral between one and eight.
 4. The dice game of claim 1 wherein each of said first die and said second die are a regular, convex polyhedra comporting with Euler's equation.
 5. The dice game of claim 1 wherein said plurality of bet lines includes at least one of a pass line, a don't pass line, a field line, a come line, a don't come line, a proposition bet line, and one or more point boxes.
 6. The dice game of claim 1 wherein said first die, said second die, and said gaming table are implemented electronically.
 7. The dice game of claim 6 wherein said electronic implementation is performed on one of a hand-held gaming device, a television-based game system, a stand-alone video machine, a personal computer, or an on-line network connection.
 8. The dice game of claim 6 wherein electronic implementation of said first die and said second die includes a module operable to model a roll result for each of said first octahedron die and said second octahedron die, said module including instructions for: establishing eight equally sized ranges between zero and one, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one possible roll result for one of said octahedron die; randomly sampling a uniformly distributed number between zero and one; selecting the range containing said sampled uniformly distributed number; providing said roll result associated with said selected range for said first octahedron die; and repeating said randomly sampling, said selecting, and said providing for said second octahedron die.
 9. The dice game of claim 6 wherein said electronic implementation of said first die and said second die includes a module operable to model a roll total for said first and second octahedron dice, said module including instructions for: establishing a plurality of ranges, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one of a plurality of possible roll totals; randomly sampling a uniformly distributed number; selecting the range containing said sampled uniformly distributed number; and providing said roll total associated with said selected range.
 10. A method of playing a dice game, comprising: placing a wager on at least one bet line of a croupier-type gaming table; rolling a pair of octahedron dice, wherein the first octahedron die provides a first result, the second octahedron die provides a second result, and the sum of said first result and said second result represents a roll total; and determining if said wager wins, loses, or pushes in response to at least one of the first result, the second result, and the roll total.
 11. The method of claim 10 wherein said rolling a pair of octahedron dice comprises: rolling a first die having eight faces numbered one through eight; and rolling a second die having eight faces numbered one through eight, wherein said first die and second die are identical.
 12. The method of claim 10 wherein said rolling a pair of octahedron dice comprises rolling a pair of dice which are regular, convex polyhedra comporting with Euler's equation.
 13. The method of claim 10 wherein said placing a wager includes placing a wager on at least one of a pass line, a don't pass line, a field line, a come line, a don't come line, a proposition bet line, and one or more point boxes.
 14. The method of claim 10 wherein said placing, rolling, and determining are performed electronically.
 15. The method of claim 10 wherein said placing, rolling, and determining are performed electronically on one of a hand-held gaming device, a television-based game system, a stand-alone video machine, a personal computer, or an on-line network connection.
 16. The method of claim 14 wherein said electronic performance of rolling a pair of octahedron dice includes: establishing eight equally sized ranges between zero and one, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one possible roll result for one of said octahedron die; randomly sampling a uniformly distributed number between zero and one; selecting the range containing said sampled uniformly distributed number; providing said roll result associated with said selected range for said first octahedron die; and repeating said randomly sampling, said selecting, and said providing for said second octahedron die.
 17. The method of claim 14 wherein said electronic performance of rolling a pair of octahedron dice includes: establishing a plurality of ranges, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one of a plurality of possible roll totals; randomly sampling a uniformly distributed number; selecting the range containing said sampled uniformly distributed number; and providing said roll total associated with said selected range.
 18. A method for modeling a roll of a pair of octahedron dice, said method comprising: establishing a plurality of ranges, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one of a plurality of possible roll totals; randomly sampling a uniformly distributed number; selecting the range containing said randomly sampled, uniformly distributed number; and providing said roll total associated with said selected range.
 19. The method of claim 18 wherein said establishing a plurality of ranges comprises: determining the probability of rolling each of said plurality of possible roll totals, the sum of all of said probabilities being equal to one; creating a plurality of ranges between zero and one, wherein the size of each of said plurality of ranges is dependent upon the probability of rolling its associated possible roll total and wherein none of said plurality of ranges overlap with another of said plurality of ranges.
 20. The method of claim 19 wherein said randomly sampling a uniformly distributed number further comprises selecting a number between zero and one.
 21. The method of claim 18 wherein said randomly sampling a uniformly distributed number comprises using a uniform random number generator.
 22. A method for modeling a roll of a plurality of octahedron dice, said method comprising: determining a roll result for one octahedron die, wherein said determining comprises: establishing eight equally sized ranges between zero and one, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one possible roll result for said one octahedron die; randomly sampling a uniformly distributed number between zero and one; selecting the range containing said sampled uniformly distributed number; and providing said roll result associated with said selected range; repeating said determining for each of said remaining plurality of octahedron dice.
 23. The method of claim 22 further comprising summing the roll result for each of said plurality of octahedron dice to obtain a roll total.
 24. The method of claim 22 wherein said establishing eight equally sized ranges comprises: creating a first range greater than or equal to zero but less than or equal to 0.125; creating a second range greater than 0.125 but less than or equal to 0.250; creating a third range greater than 0.250 but less than or equal to 0.375; creating a fourth range greater than 0.375 but less than or equal to 0.500; creating a fifth range greater than 0.500 but less than or equal to 0.625; creating a sixth range greater than 0.625 but less than or equal to 0.750; creating a seventh range greater than 0.750 but less than or equal to 0.875; and creating a eighth range greater than 0.875 but less than or equal to 1.000.
 25. The method of claim 22 wherein said randomly sampling a uniformly distributed number between zero and one comprises using a uniform random number generator.
 26. A module containing an ordered set of instructions that when executed perform a method of playing a dice game, said method comprising: receiving wager information; electronically providing at least one of a first result for a roll of a first octahedron die, a second result for a roll of a second octahedron die, and a roll total, said roll total equaling the sum of said first result and said second result; and determining if the wager wins, loses, or pushes in response to at least one of the first result, the second result, and the roll total.
 27. The module of claim 26 wherein said method further comprises maintaining a tally of wins, losses, and pushes.
 28. The module of claim 26 wherein said method further comprises crediting and debiting an account in response to said determining step.
 29. The module of claim 26 wherein said method further comprises dispensing cash or tokens in response to said determining step.
 30. A method of playing a dice game in an electronic format, comprising: inputting wager information; receiving the results of an electronic simulation of a roll of a pair of octahedron dice, wherein said results include at least one of a first result for the roll of the first octahedron die, a second result for the roll of the second octahedron die, and a roll total, said roll total equaling the sum of said first result and said second result; and receiving a determination as to whether said wager wins, loses, or pushes in response to at least one of the first result, the second result, and the roll total.
 31. The method of claim 30 wherein said method further comprises receiving a tally of wins, losses, and pushes.
 32. The method of claim 30 wherein said method further comprises crediting and debiting an account in response to said receiving a determination step.
 33. The method of claim 30 wherein said receiving the results of an electronic simulation of a roll of a pair of octahedron dice comprises receiving the results of a module executing a set of instructions for: establishing a plurality of ranges, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one of a plurality of possible roll totals; randomly sampling a uniformly distributed number; selecting the range containing said sampled uniformly distributed number; and providing the roll total associated with said selected range.
 34. The method of claim 30 wherein said receiving the results of an electronic simulation of a roll of a pair of octahedron dice comprises receiving the results of a module executing a set of instructions for: establishing eight equally sized ranges between zero and one, wherein each range contains at least one uniformly distributed number and wherein each range is associated with one possible roll result for one of said octahedron die; randomly sampling a uniformly distributed number between zero and one; selecting the range containing said sampled uniformly distributed number; providing the roll result associated with said selected range for the first octahedron die; and repeating said randomly sampling, said selecting, and said providing for the second octahedron die. 